Here we describe how to build a projection of the 16 cell, one of the six regular polytopes in 4-dimensional space, using the zometool system. For the model you need

  • 8 balls,
  • 6 long blue (b2) struts,
  • 6 long red (r2) struts,
  • 6 medium red (r1) struts,
  • 6 long yellow (y2) struts.

Of course one can scale down the model to b1-r1-r0-y1, but this becomes quite tiny.

For further information and instructions you might also wish to consult one of the following webpages:

The pictures below were taken by Eva-Maria Gassner.

Step 1

Use the blue and the medium red struts to build two regular triangles with small red pyramids mounted on top.

Step 2

Take the 6 yellow struts. Mount 3 of them inwards pointing on the vertices of the blue triangle. The others are mounted outwards pointing at the tip of the blue-red pyramid.

Step 3

On the vertices of the blue triangle put long red struts that are pointing to the endpoints of the outward pointing yellow struts.

Step 4

Complete the model by mounting the second blue-red pyramid from step 1 on the loose ends of the red and yellow struts constructed in step 2 and 3.

This Zometool model of the 16 cell shows all of the 16 tetrahedral cells, but they appear differently squashed as a result of the projection. Moreover, in contrast to the vertex-first projection all of the 8 vertices and all of the 24 edges are visible in this projection.

This model is connected to the other two models (see here and here) by the Zometool Triality.